When did the inhabitants of Italy start considering themselves italian -and why?
The idea of Italy as a geographic area and cultural block dates to the post-Roman era, and was prevalent even in the disunited middle ages and early modern era. For example, in the negotiations of the Peace of Utreicht after the War of Spanish succession in 1713, the Venetian Ambassador Carlo Ruzzini reported that the Republic of Venice was seen as "La Principale Potenza e Protettrice d'Italia" or "Principal Power and Protector of Italy."
However, the idea of Italy as a politically unified entity only dates to the 19th century.
The French Emperor Napoleon, through his conquest of the ten 18th century successors of the medieval Italian city-states, lay the definitive foundation for what would become modern Italy. After Napoleon’s conquest of the peninsula, Northwestern Italy was integrated with the French Empire, while the northeast proclaimed "The Kingdom of Italy," with Napoleon crowned king. The south remained the Kingdom of Naples, and was ruled by Napoleon’s brother-in-law, Joachim Murat. In all three polities, Napoleon abolished old ecclesiastical and aristocratic privileges and imposed uniform legal, administrative, and fiscal laws and institutions. Devoid of economic or customs barriers, and in spite of the three-way administrative division, Italy under Napoleon was united for the first time in hundreds of years.
Following the repression of the post-Napoleonic restoration, intellectuals from all over Italy migrated to the Kingdom of Piedmont-Sardinia (many, especially those with middle-class origins, had rapidly risen in the ranks of the meritocratic Napoleonic administration). Although initially repressive, the government in Turin soon cautiously acknowledged their value. One of the more marginal states in Italian history, the Piedmontese already had a precedent for acknowledging and adopting the practices of their more powerful neighbors; welcoming prominent exiles wasn’t too much of a stretch. These intellectuals would not only supply the Turinese government with a full roster of capable public administrators who fueled its economic life, they gradually enticed Piedmont it to take action bringing about the unification of Italy.
Davis, John A. Italy in the Nineteenth Century, 1796-1900. Oxford: Oxford UP, 2000.
As a follow-up, was there a concept of an "Italy" of some sort before there was a concept of an "Italian people," and what were the earliest attempts to create a united Italy?
After the beginning of the Social War in 91 B.C. the enemies of Rome, once socii of Rome, cities and populations allied with Rome, changed the name of their league in Italic League.
Also they began minting a shared currency, on some of the coins is visible the world "Italia".
These were pointed out by my professor of Roman History to be some of the earliest signs of the emergence of the concept of Italy.